Use our free GCF of Fractions Calculator tool to compute the GCF of 44/288, 305/640, 361/300 i.e 1/28800 easily. The following is the detailed procedure to determine the greatest common factor of fractions 44/288, 305/640, 361/300.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 44/288,305/640,361/300
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 44/288,305/640,361/300, numerators are 44,305,361
Denominators are 288,640,300
The GCF of 44,305,361 is 1 .
LCM of 288,640,300 is 28800.
The greatest common factor of 44/288,305/640,361/300 = [GCF of 44,305,361]/[LCM of 288,640,300]= 1/28800
Therefore, the GCF of 44/288,305/640,361/300 is 1/28800.
To find the highest common factor of 44,305,361, we have to find the factors of both numbers and list the highest common factor.
The factors of 44 are 1, 2, 4, 11, 22, 44
The factors of 305 are 1, 5, 61, 305
The factors of 361 are 1, 19, 361
The HCF of 44,305,361 is 1.
Lets's calculate GCF of 44,305,361
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 44
:1,2,4,11,22,44
Now, list down the factors of 305
:1,5,61,305
Now, list down the factors of 361
:1,19,361
Greatest Common Factor
We found the factors 44,305,361 . The biggest common factor number is the GCF number.
So the greatest common factor 44,305,361 is 1.
Lets's calculate LCM of 288,640,300
2 | 288, 640, 300 |
2 | 144, 320, 150 |
2 | 72, 160, 75 |
2 | 36, 80, 75 |
2 | 18, 40, 75 |
3 | 9, 20, 75 |
5 | 3, 20, 25 |
3, 4, 5 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 3 x 5 x 3 x 4 x 5 = 28800
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/28800
Therefore, the GCF of Fractions 44/288,305/640,361/300 is 1/28800
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 288,640,300 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(288,640,300) = 4
common factors(in case of two or more numbers have common factors) = 480
GCF(288,640,300) x common factors =4 x 480 = 1920
LCM(288,640,300) = ( 288 × 640 × 300 ) / 1920
LCM(288,640,300) = 55296000 / 1920
LCM(288,640,300) = 28800
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 44,305,361?
The HCF of 44,305,361 is 1
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 44/288, 305/640, 361/300?
Answer: GCF of Numerators as per given numbers 44/288, 305/640, 361/300 is
GCF of Numerators i.e. for 44,305,361 is 1
LCM of denominators i.e. for 288,640,300 is 28800.
Thus, GCF of Fractions is 1/28800.Finally, GCF of Fractions for 44/288, 305/640, 361/300 is 1/28800.